The former England international, who turns 31 next week, made his first start since the Europa League qualifier against Gomel on August 2 but lasted just 45 minutes.

He was withdrawn at half-time for captain Steven Gerrard with Rodgers admitting former Swans star Joe Allen was the only midfielder to perform well in the opening 45 minutes.

Chico Flores and Nathan Dyer put the visitors 2-0 up and, although another interval substitute Luis Suarez quickly reduced the deficit, Jonathan de Guzman added a third in added time.

"The club have invested an astronomical amount of money on a talented player and Joe had the opportunity," said Rodgers.

"He has been back fit a couple of weeks and his opportunities have been limited but you have to see.

"I thought it was difficult for him, it was too slow and it wasn't what I would expect from a team I tried to set up to be dynamic."

Cole, signed on a free transfer from Chelsea by Roy Hodgson on wages of £100,000 a week, spent last season on loan at Lille.

He returned to Anfield this summer determined to make an impression on a manager he knew from their time together at Stamford Bridge but he is just not fitting in and further first-team chances appear slim.

Rodgers was unhappy with his side's first-half performance in particular and was gracious to admit his former club deserved their victory.

"I thought the best team won. We were too slow, there was no tempo in the first half," admitted the Northern Irishman, who left south Wales to take over from Kenny Dalglish at Anfield in June.

"It is disappointing. You can only hurt (from the result) if you are the better team and I thought they were the better team.

"I am disappointed to be out of the competition but I don't think we can have any complaints."

Swansea boss Michael Laudrup, having succeeded Rodgers, hailed the club's achievement of reaching the quarter-finals of the competition for the first time.

"I think we deserved the win and it is not very often you can say that as a manager playing at Anfield against Liverpool," said the former Denmark international, whose side now have a home tie against npower Championship side Middlesbrough.

"To win at Anfield is great so maybe it is (the best performance of his short reign).

"For 80 minutes we played a really good game with some fantastic counter-attacks and it was nice to watch.

"It is the first time the club has gone so far in the competition and to be in the last eight is great.

"It is a great achievement for the squad and the fans and now we can enjoy it but not for too long because we have another big game at Chelsea."